BECE Mathematics 2010 Paper

Concept:The circumference of a circle is found using the radius, which is obtained from the given area.Explanation:The formula for the area of a circle is $A = \pi r^2$, where $r$ is the radius.It is given that $A = 64\pi \ \text{cm}^2$.Therefore, $\pi r^2 = 64\pi \ \text{cm}^2$.Cancel $\pi$ from both sides to get $r^2 = 64 \ \text{cm}^2$.Since $64 = 8^2$, we have $r^2 = (8\ \text{cm})^2$.Taking the positive square root gives $r = 8\ \text{cm}$.The circumference of a circle is given by $C = 2\pi r$.Substitute $r = 8\ \text{cm}$: $C = 2\pi \times 8\ \text{cm}$.This simplifies to $C = 16\pi \ \text{cm}$.Answer:The circumference of the circle is $16\pi \ \text{cm}$.